NEET Oscillations — Set 17

Question 1

Which statement correctly describes the relationship between SHM and uniform circular motion?

Accepted Answer

SHM is the one-dimensional projection of uniform circular motion along a diameter, with the same period but different force characteristics (linear vs. centripetal).

Question 2

A spring-mass system has $ m = 2 \, \text{kg}, k = 800 \, \text{N/m} $. What is its angular frequency?

Accepted Answer

$ \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{800}{2}} = \sqrt{400} = 20 \, \text{rad/s} $.

Question 3

Which of the following represents periodic motion but not SHM? ($ \omega $ is a positive constant)

Accepted Answer

(a) $ 2 \cos (\omega t) $: SHM. (b) $ \cos \omega t + \cos 3\omega t $: Periodic (period $ \frac{2\pi}{\omega} $), not SHM (multiple frequencies). (c) $ 3 \sin (2\omega t) $: SHM. (d) $ e^{-\omega t} $: Not periodic.

NEET Physics: Oscillations — Practice Set 17

Q1. Which statement correctly describes the relationship between SHM and uniform circular motion?

Q2. A spring-mass system has \( m = 2 \, \text{kg}, k = 800 \, \text{N/m} \). What is its angular frequency?

Q3. Which of the following represents periodic motion but not SHM? (\( \omega \) is a positive constant)

Q4. Two identical springs (\( k = 100 \, \text{N/m} \)) are attached to a \( 2.0 \, \text{kg} \) mass as in Fig. 13.14. What is the period?

Q5. A spring of \( k = 200 \, \text{N/m} \) has a \( 0.5 \, \text{kg} \) mass. If \( E = 1 \, \text{J} \), what is the amplitude?

Q6. A mass oscillates with \( v = -8 \cos (2t) \) (in m/s). What is its displacement function?

Q7. What happens to the period of a spring-mass system if both the mass and spring constant are doubled?

Q8. A mass of \( 0.5 \, \text{kg} \) on a spring has \( E = 2 \, \text{J} \) at \( A = 20 \, \text{cm} \). What is the spring constant?

Q9. A spring-mass system oscillates with \( T = 0.4 \, \text{s} \) when \( m = 0.2 \, \text{kg} \). What is the spring constant?

Q10. A mass of \( 4 \, \text{kg} \) is attached to a spring with \( k = 1600 \, \text{N/m} \) and displaced by \( 5 \, \text{cm} \). What is the total energy?